The short answer is yes if the Office 365
subscription plan includes the Desktop applications.
What has make it confusing for me is that you have said that you want to to (run) on Office 365. That would men you want to use thr hosted servers of Exchange, Sharepoint, Lync, and OneDrive.
I think your confusion may come from thinking that Office 365 is a product, It is not a product but a subscription plan which includes a combination of products and/or services.
Your plan could include the desktop office apps which is all the programs included in Office Professional Plus suite. That means you can do everything you could do if you purchases the desktop Office Professional Plus software separately.
Note: Office 365 is generally the cheapest what to get Office Professional Plus desktop suite and always have the current version. That is the office suite included with any Office 365 plan that includes the desktop applications! And you always get the current release plus more depending on the plan.
What Office 365 plans provide is other additional products or services. Like additional OneDrive online disk space for storing and sharing files. One Drive also included Word, Excel, and Powerpoint online versions. The business plan can also include hosted Exchanges, Sharepoint, and Lync serves.
Another way to think of the Office 365 Plan subscriptions is lie like Cell Phone plans. Your plan can includes cell minutes, texting, data usage, online file storage, etc. You chose the plan that has the combination of services you need.
If you want to get Office 203 Professional Plus then the Office
365 Business plan includes full Office desktop plus extra OneDrive space over a free account.
This plan does NOT include and hosted servers Exchange, Sharepoorint, or Lync.
The Office 365 Business plan is basically a subscription to Office Professional Plus desktop apps.
See:
https://products.office.com/en-us/b...5SMB_office 365 business plans_Text&WT.srch=1
Office 365 Business plan is just another way to get the Office Professonal Plus office suite on the desktop!
see attached image.
Hopefully this helps ...